On-field temperatures hit 100 degrees, bur the U.S. team put together another excellent overall performance, out-shooting the Brazilians, 19-10.
Rodriguez, a halftime sub, crushed a rising shot into the roof of the net at the near post from 10 yards out after a cross by Abby Wambach skipped through the legs of a Brazilian defender and took a slight deflection right into Rodriguez's path.
"I said at halftime to take the chance and keep possession," said U.S. head coach Pia Sundhage. "You feel like you are under pressure, but [the USA] is such a good team that we can keep possession under pressure and let them run instead. I think we did that in the second half. The fact that we were more patient, kept possession in the midfield and in the back, and at the same time we had A-Rod up top. That was the difference in the second half."
The USA will travel to San Diego to face Brazil on Wednesday in the second match of this two-leg series and the last before it heads to the 2008 Olympics (TV: Fox Soccer Channel, live, 10 pm ET).
July 13 in Commerce City, Colo.
USA 1 Brazil 0. Goal: Rodriguez 71.
USA -- Solo (Barnhart, 46), Chalupny, Rampone, Markgraf (Buehler, 83), Mitts Cox, 46), Boxx (Wagner, 83), O'Reilly (Heath, 62), Tarpley (Hucles, 46), Lloyd, Kai (Rodriguez, 46), Wambach.
Brazil -- Andrea (Barbara, 46), Jatoba (Maurine, 75), Tania, Erika (Andreia Rosa, 12), Formiga, Maicon, Ester, Francielle (Rosana, 42; Daiane, 87), Renata Costa, Pretinha (Raquel, 57), Fabiana (Pitty, 59).
Referee: Dallas Malhiwsky (USA).